Linear quadratic control of plane Poiseuille flow-the transient behaviour.

Abstract

This paper describes the design of optimal linear quadratic controllers for single wavenumber-pair periodic 2-D disturbances in plane Poiseuille flow, and subsequent verification using a finite-volume full Navier-Stokes solver, at both linear and non-linear levels of initial conditions selected to produce the largest linear transient energy growth. For linear magnitude initial conditions, open and closed-loop finite-volume solver results agree well with a linear simulation. Transient energy growth is an important performance measure in fluid flow problems. The controllers reduce the transient energy growth, and the non-linear effects are generally seen to keep energy levels below the scaled linear values, although they do cause instability in one simulation. Comparatively large local quantities of transpiration fluid are required. The modes responsible for the transient energy growth are identified. Modes are shown not to become significantly more orthogonal by the application of control. The synthesis of state estimators is shown to require higher levels of discretiation than the synthesis of state-feedback controllers. A simple tuning of the estimator weights is presented with improved convergence over uniform weights from zero initial estimates